Laboratory Report: Pressure Measurement

Categories: Physics

Report, Pages 3 (606 words)

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Experiment #1

Objective

The objective of this experiment is to demonstrate different pressure measurement methods. It involves using U-tube and inclined tube manometers, as well as calibrating a Bourdon tube manometer using a dead weight piston gauge.

Theory

Pressure (symbol: p or P) is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It is typically measured in units such as N/m², Pa, or psi. Absolute pressure (p_abs) is measured relative to absolute zero pressure, which is the pressure at absolute vacuum.

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For gas law calculations, pressure and temperature must be in absolute units.

A gauge is often used to measure the pressure difference between a system and the surrounding atmosphere, known as gauge pressure (p_g), which can be calculated as:

p_g = p_s - p_atm ... (2)

Where:
p_g = gauge pressure
p_s = system pressure
p_atm = atmospheric pressure

U-tube manometers are commonly used to measure pressure differences between containers or points in a system, while Bourdon pressure gauges deform elastically in response to applied pressure, allowing pressure measurement for fluids.

Equipments Used

U-tube manometer
Inclined U-tube manometer
Bourdon Gage Manometer
Syringes

Procedure

The pressure changes in the U-tube and inclined U-tube manometers were measured by applying air pressure using a syringe at different volumes (1cc and 3cc).

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The obtained values were averaged, and standard deviation was calculated to assess experimental errors.

The standard deviation ( ) is calculated using the following formula:

= √[Σ(xi - x̄)² / (n - 1)]

Where:
= standard deviation
xi = individual data point
x̄ = mean value
n = number of data points

Calculated Data

The following data was obtained using U-tube, inclined U-tube manometers, and Bourdon gage:

Table 1: Data for U-tube manometers

Manometer Type	∆h (mm)	Pressure (bars)	Inclined U-tube Manometer	∆h (mm)	Pressure (bars)
1cc Syringe	69	6.51±2.61	65.79	67.106±1.29	6.58±1.29
2cc Syringe	66	6.51±2.61	65.79	67.106±1.29	6.58±1.29
3cc Syringe	65	6.51±2.61	65.79	67.106±1.29	6.58±1.29

Table 2: Data for Bourdon gage

Sample	Weight (g)	P calculated (bar)	P label (bar)	P reading (bar)	P (corrected) (bar)
-	-	0.30 ± 0.025	0.0 ± 0.025	0.14 ± 0.025	-
1	191.4	0.166	0.166 ± 0.002	0.60 ± 0.025	0.16 ± 0.025
2	574.9	0.4987	0.50 ± 0.002	0.94 ± 0.025	0.50 ± 0.025
3	766.3	0.6647	0.666 ± 0.004	1.10 ± 0.025	0.66 ± 0.025
4	1148.8	0.9965	1.00 ± 0.004	1.43 ± 0.025	0.99 ± 0.025
5	2294.6	1.4916	1.50 ± 0.006	1.92 ± 0.025	1.48 ± 0.025
Unknown	-	x	-	0.94 ± 0.025	0.50 ± 0.025

Note: The density of the fluid is equal to the density of water.

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The inclination angle is 60°, and the diameter of the piston is 12 mm. The weight of the carrier is 519 g.

Analysis

Table 1 provides a comparison of pressure changes in the manometers when external air pressure was applied using 1cc and 3cc of air. Pressure is calculated as p = ρg∆h in Pascal.
We can observe from the table that as the volume of air added increases, the pressure change in the manometers also increases for both types. The inclined U-tube manometer yields greater accuracy due to its smaller calibrations.
A linear relationship between P(corrected) and weight can be drawn from Table 2. This relationship aligns with expectations, as an increase in force on a specific area leads to an increase in pressure. The graph includes error bars to account for uncertainties.
The calculated pressure values and those labeled on the Bourdon Gage are closely matched in Table 2, with small differences potentially attributed to experimental errors.
An unknown weight was tested, yielding a pressure reading of 0.5 ± 0.025 bars. From the graph, the weight reading is determined to be 1.1 kg, indicating the unknown weight is 0.571 kg or 571 g.

Conclusion

In conclusion, pressure measurement using manometers is a widely utilized and accurate technique. The experimental results closely match the expected values, with minor variations potentially attributable to experimental errors. It is worth noting that the Bourdon Gage Manometer had an initial calibration error of 0.3 bars, which may have resulted from air bubbles in the piston linings. This brief experiment required minimal effort but ensured reliable results through the acquisition of multiple manometer readings. Additionally, uncertainties were incorporated into calculations to enhance result accuracy.